How powerful is Great Britain really?

Never-ever underestimate your country mate.

As somebody has already said, the British Army IS the best trained Army in the world - FACT. We along with France and the US are one of only three countries who have a blue water Navy. Our RAF pilots are very skilled and have some of the most advanced aircraft on the planet (The Eurofighter Typhoon recently beat the US F22 Raptor in a head to head mock dogfight for training purposes. (OEU trials) The next day the US canceled further tests and is believed to be the reason why the British company BAE Systems has the contract to update the computer systems on the F22).

We are the Head of the British Commonwealth. 53 countries (including Canada, Australia and New Zealand) that make over a third of the world population. These countries are sworn to protect us if anyone attacked and they call our Queen their Queen too (so our Queen is the Queen of Austrailia too).

Nobody will ever conquer us we are not as powerful as we once were - but we are still vey powerful.

In reality and practice about the same as NY State and City or LA city and CA State.

Given an election landslide to an Independent British party we would be independently on a par w. Italy and France (the US would take back Trident (they have always kept the launch codes) if we didn't stay in their back pocket) but in a world wide nuclear exchange if most of the N. Hemisphere was made uninhabitable it would be the old British Empire colonies of Australia and NZ allied w. Brazil that would effectively bring Great Britain back on top down under (worldwide). Some of Canada would probably remain operational and they have always been proud to be British first and foremost.

As in politics and life the answer depends entirely on events!

After World War II Britain basically gave up most of its empire and military

The British army is the best trained in the world so they say...but yeah we gave up alot of Empire after the 2nd world war.

Not very, really. Compared to EU powers, they hold their own. Compared to the US and China, they aren't. Measuring power by how much control they have over their own willing citizens doesn't say much.